Question

find the first three partial sums of the series.
9 + 14 + 19 + 24 + 29 + 34 + ...
write your answers as integers or fractions in simplest form.
s₁ =
s₂ =
s₃ =

Explanation:

Step1: Find \( S_1 \)

The first partial sum \( S_1 \) is just the first term of the series. The first term is 9, so \( S_1 = 9 \).

Step2: Find \( S_2 \)

The second partial sum \( S_2 \) is the sum of the first two terms. So we add the first term (9) and the second term (14): \( S_2 = 9 + 14 = 23 \).

Step3: Find \( S_3 \)

The third partial sum \( S_3 \) is the sum of the first three terms. We add the first term (9), the second term (14), and the third term (19): \( S_3 = 9 + 14 + 19 = 42 \).

Answer:

\( S_1 = 9 \)
\( S_2 = 23 \)
\( S_3 = 42 \)